It is a time consuming process to construct in 2D or in 3D space a graphical representation of an object which includes segments of an intersection of a modular matrix of rectangles and an elliptic, lenticular or rhombic segment. A modular matrix of rectangles consists of rows and columns of modular spaced equal rectangles. The spacing module of the rows is independent of the spacing module of the columns. Objects which include segments of an intersection of a modular matrix of rectangles and an elliptic, lenticular or rhombic segment may be part of complex geometric designs for example used in architecture for doors, windows or other applications.
At present, to generate an image incorporating segments of an intersection of a modular matrix of rectangles and an elliptic, lenticular or rhombic segment requires that the location of the vertices of the resulting segments is solved before the representation is drawn either on paper or on a computer. However, the image so created is specific to the attributes which are given (length, width, number of columns and rows of rectangles and the like), and cannot be used except with those attributes. Changing any value of the attributes of the modular matrix of rectangles or of the elliptic, lenticular or rhombic segment such as the spacing and/or widths of the rectangles or the aspect ratio of the elliptic, lenticular or rhombic segment, usually requires redrawing the entire image of the intersection of a modular matrix of rectangles and an elliptic, lenticular or rhombic segment.
To alleviate this problem computer graphics systems sometimes include a database with geometric data for a finite number of pre-constructed instances of objects with an intersection of a modular matrix of rectangles and an elliptic, lenticular or rhombic segment. The usability of such graphic system remains limited to the selection of those instances which are stored in the database. Changing the total width or length of such pre-constructed object may result in a degeneration of the selected geometry which the user cannot correct. Such degeneration, in the context of a computer graphics system for design, such as an architectural modeling program, is clearly unacceptable, because of the loss of dimensional accuracy and the geometrical distortion which results.